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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Geometric programming ： ウィキペディア英語版 Geometric programming A geometric program (GP) is an optimization problem of the form : Minimize $\backslash \; f\_0(x)\backslash$ subject to :: $f\_i(x)\; \backslash leq\; 1,\; \backslash quad\; i\; =\; 1,\backslash dots,m$ :: $h\_i(x)\; =\; 1,\backslash quad\; i\; =\; 1,\backslash dots,p$ :where $f\_0,\backslash dots,f\_m$ are posynomials and $h\_1,\backslash dots,h\_p$ are monomials. In the context of geometric programming (unlike all other disciplines), a monomial is defined as a function $f:\backslash mathbb\_^n\; \backslash to\; \backslash mathbb$ defined as :$f(x)\; =\; c\; x\_1^\; x\_2^\; \backslash cdots\; x\_n^$ where $c\; >\; 0\; \backslash$ and $a\_i\; \backslash in\; \backslash mathbb$. GPs have numerous application, such as components sizing in IC design〔http://www.stanford.edu/~boyd/papers/opamp.html〕 and parameter estimation via logistic regression in statistics. The maximum likelihood estimator in logistic regression is a GP. ==Convex form== Geometric programs are not (in general) convex optimization problems, but they can be transformed to convex problems by a change of variables and a transformation of the objective and constraint functions. In particular, defining $y\_i\; =\; \backslash log(x\_i)$, the monomial $f(x)\; =\; c\; x\_1^\; \backslash cdots\; x\_n^\; \backslash mapsto\; e^$, where $b\; =\; \backslash log(c)$. Similarly, if $f$ is the posynomial $f(x)\; =\; \backslash sum\_^K\; c\_k\; x\_1^\}$ then $f(x)\; =\; \backslash sum\_^K\; e^$, where $a\_k\; =\; (a\_,\backslash dots,a\_\; )$ and $b\_k\; =\; \backslash log(c\_k)$. After the change of variables, a posynomial becomes a sum of exponentials of affine functions. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Geometric programming」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.